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Crises and Prices: Information Aggregation, Multiplicity, and Volatility

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Crises and Prices: Information Aggregation, Multiplicity, and Volatility Crises and Prices: Information Aggregation, Multiplicity, and Volatility By GEORGE-MARIOS ANGELETOS AND IVA´ N WERNING* Crises are volatile times when endogenous sources of information are closely monitored. We study the role of information in crises by introducing a financial market in a coordination game with imperfect information. The asset price aggre- gates dispersed private information acting as a public noisy signal. In contrast to the case with exogenous information, our main result is that uniqueness may not obtain as a perturbation from perfect information: multiplicity is ensured with small noise. In addition, we show that: (a) multiplicity may emerge in the financial price itself; (b) less noise may contribute toward nonfundamental volatility even when the equilibrium is unique; and (c) similar results obtain for a model where individuals observe one another’s actions, highlighting the importance of endogenous infor- mation more generally. (JEL D53, D82, D83) It’s a love-hate relationship—economists are outcomes, but often lack obvious comparable at once fascinated and uncomfortable with mul- changes in fundamentals. Many attribute an im- tiple equilibria. On the one hand, crises can be portant role to more or less arbitrary shifts in described as times of high nonfundamental vol- “market sentiments” or “animal spirits,” and atility: they involve large and abrupt changes in models with multiple equilibria formalize these ideas.1 On the other hand, these models can also be viewed as incomplete theories, which should * Angeletos: Department of Economics, Massachusetts ultimately be extended along some dimension Institute of Technology, 50 Memorial Drive, Cambridge, MA 02142, and National Bureau of Economic Research to resolve the indeterminacy. Stephen Morris (e-mail: [email protected]); Werning: Department of Eco- and Hyun Song Shin (1998, 2001) argue that nomics, MIT, 50 Memorial Drive, Cambridge, MA 02142, this dimension is information, and that multi- NBER, and Universidad Toncuato di Tella (e-mail: plicity vanishes once the economy is perturbed [email protected]). We are grateful to the coeditor, Rich- ard Rogerson, and three anonymous referees for their com- away from the perfect-information benchmark. ments and suggestions. We also thank Daron Acemoglu, This result is obtained with an exogenous Fernando Alvarez, Manuel Amador, Olivier Blanchard, information structure, but information is largely Gadi Barlevy, Ricardo Caballero, V. V. Chari, Harold Cole, endogenous in most situations of interest. Fi- Christian Hellwig, Patrick Kehoe, Stephen Morris, Alessan- nancial prices and macroeconomic indicators dro Pavan, Bernard Salanie´, Jose´ Scheinkman, Bala`zs Szentes, Aleh Tsyvinski, and seminar participants at Boston convey information about what others are doing University, Brown University, Columbia University, Duke and thinking. These variables are monitored in- University, Georgetown University, Iowa State University, tensely during times of crisis and appear to be Harvard University, MIT, Princeton University, Stanford an important part of the phenomena. As an University, University of California-Berkeley, UCLA, the Federal Reserve Banks of Boston, Chicago, and Minneap- example, consider the Argentine 2001–2002 olis, the 2004 Minnesota Summer Workshop in Macroeco- nomic Theory, the 2004 UTDT Summer Workshop in International Economics and Finance, the 2005 NBER Eco- nomic Fluctuations and Growth meeting in San Francisco, 1 Applications range from bank runs, currency attacks, the 2005 Annual CARESS-Cowles Conference on General debt crises, and financial crashes to riots, revolutions, and Equilibrium, the 2005 Workshop on Beauty Contests in social change. See, for example, Douglas W. Diamond and Cambridge, UK, the 2005 SED meeting, and the 2005 Philip H. Dybvig (1983); Maurice Obstfeld (1986, 1996); NBER Summer Institute. We are grateful to Emily Gal- Guillermo A. Calvo (1988); Russell Cooper and Andrew lagher for valuable editorial assistance and to the Federal John (1988); Harold L. Cole and Timothy J. Kehoe (1996); Reserve Bank of Minneapolis for their hospitality during the Andre´s Velasco (1996). Cooper (1998) provides excellent time the revision for this paper was completed. review. 1720 VOL. 96 NO. 5 ANGELETOS AND WERNING: CRISES AND PRICES 1721 crisis, which included devaluation of the peso, default on sovereign debt, and suspension of bank payments. Leading up to the crisis, the peso-forward rate and bank deposits deterio- rated steadily throughout 2001. This was widely reported by news media and investor reports, and closely watched by people making impor- tant economic decisions. The aim of this paper is to understand the role of endogenous information in crises. We focus on two distinct forms of nonfundamental vola- tility. First, we investigate the existence of mul- tiple equilibria, since sunspots could then create volatility unrelated to fundamentals. Second, for situations with a unique equilibrium, we examine the sensitivity of outcomes to nonfun- FIGURE 1. REGIONS OF MULTIPLICITY AND UNIQUENESS damental disturbances, namely, aggregate noise ␴ Note: x measures the exogenous noise in private iniforma- in public sources of information. We argue that tion, and ␴␧ the exogenous noise in the aggregation of endogenizing public information is crucial for information. understanding both sources of volatility. The backbone of our model is the coordina- tion game that Morris-Shin and others have plicity in the exogenous parameter space of our ␴ used to capture applications such as currency cri- model. On the vertical axis, x represents the ses, bank runs, and financial crashes. We intro- noise in private information; on the horizontal duce a financial market where individuals trade axis, ␴␧ represents the noise in the aggregation using their private information. The rational- process, namely, the randomness in asset sup- ␴ ␴ expectations equilibrium price aggregates dis- ply. Multiplicity obtains when either x or ␧ is perse private information, while avoiding perfect sufficiently small. revelation due to unobservable supply shocks as in In our baseline model, the asset’s dividend Sanford J. Grossman and Joseph E. Stiglitz (1976). depends merely on the exogenous fundamen- This price is our endogenous public signal. tals. The financial market then provides infor- The main insight to emerge is that the preci- mation relevant for the coordination game, but sion of endogenous public information in- there is no feedback in the opposite direction. In creases with the precision of exogenous private an extension, we allow for such a feedback by information. When private signals are more pre- considering the possibility that the dividend de- cise, individuals’ asset demands are more sen- pends on the outcome of the coordination game. sitive to their information. As a result, the This may capture, in a stylized fashion, the real equilibrium price reacts relatively more to fun- rate of return on peso-forwards during currency damental than to nonfundamental variables, attacks, or more generally stock-market returns conveying more precise public information. during economic crises. Interestingly, multiplic- This has important implications for the deter- ity then emerges in the equilibrium price. minacy of equilibria. The endogenous increase This is easily explained. In equilibrium, the in the precision of public information permits price affects the coordination outcome; the out- agents to better forecast one another’s actions come in turn affects the dividend; hence, the and thereby makes it easier to coordinate. Con- dividend itself is a function of the price. Since a sequently, uniqueness need not obtain as a per- higher price can lead to a higher dividend, the turbation away from the perfect-information demand for the asset is backward bending, giv- benchmark. Indeed, in our baseline model, mul- ing rise to multiple intersections with supply. tiplicity is ensured when noise is small. Motivated by bank runs and riots, we also This result is illustrated in Figure 1, which consider a model where individuals do not trade displays the regions of uniqueness and multi- a financial asset, but instead directly watch over 1722 THE AMERICAN ECONOMIC REVIEW DECEMBER 2006 what others are doing: everyone observes a noisy considers a similar application, but focuses on signal of the average action in the population. This conditions that deliver a unique equilibrium. introduces endogenous public information in the The information structure is also endogenous Morris-Shin framework parsimoniously, with- in Angeletos et al. (forthcoming, 2006), but in out the need for modeling a financial market. It different ways. They examine, respectively, sig- also brings a main element of herding models, naling effects in a policy game and the interplay the observation of other players’ actions, into between information and crises in a dynamic coordination games. Of course, this framework setting. Amil Dasgupta (forthcoming) intro- cannot address multiplicity or volatility in the duces signals of others’ actions in an investment financial market. However, our results on re- game, as in Section IV of this paper, but as- gime-outcome multiplicity carry over here, sumes that these signals are entirely private highlighting information aggregation as the key instead of public, thus abstracting from the role mechanism, not any particular form of it. of endogenous information for multiplicity of Results on multiplicity are of interest be- equilibria. cause
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